Fewer than one in 10 people is putting money aside for care and support in old age, according to a survey that shows the huge scale of the challenge facing policy-makers in reforming the care funding system.

Almost half those surveyed still think the government should cover all care costs for elderly people, despite repeated assertions by all the main political parties that people must make a substantial contribution if they have the means to do so.

The survey, by ICM for housing and care charity Anchor, demonstrates the difficult task that ministers will have if they move to reform the funding system for England and Wales in line with the likely recommendations of an official review due to report next week.

The review, led by the economist Andrew Dilnot, is thought to have ruled out any idea of free care for those with the means to pay. Although it is expected to propose capping individual liability at £35,000, excluding non-care costs for accommodation, people would be required to pay up to that level and would be encouraged to save or to insure themselves to do so.

Jane Ashcroft, the chief executive of Anchor, said: "We know that care funding is facing a black hole, but our research suggests that the Dilnot commission's findings will be met with a hostile reaction from the public."

The survey, of 2,000 adults across Britain, found that 44% believed the government "should cover all social care costs for older people". In Scotland, where a limited form of free personal care is offered, the proportion rose to 50%.

Just 6% said they were already "saving for social care in later life" and only 8% said they would willingly sell their home to pay for care.

Asked if people should pay into a dedicated "care pension" or insurance scheme to fund their care in old age, only 25% agreed. But just 14% said they would be willing to pay higher taxes to underwrite the social care system, suggesting people have only a limited grasp of the trade-offs that experts say are central to any reform.

Ashcroft said ministers needed to acknowledge that the Dilnot recommendations would not be the end of the road, but merely the first step in a long journey to creating a sustainable new system.

"While it is vital that the government does not sweep this issue under the carpet, as previous administrations have done, it also needs to learn the lessons from the revolt over the health and social care bill and listen carefully to what the public, and the experts, are saying."

Local authority leaders are warning that the government must act on Dilnot. In a declaration and letter to the main political parties, released at the start today of the Local Government Association's annual conference, they say that "councils will not accept another missed opportunity".